Crystal Chemistry and Physics of UCd11

In the phase diagram U-Cd, only one compound has been identified so far—UCd11 (space group Pm3̅m). Since the discovery of this material, the physical properties of UCd11 have attracted a considerable amount of attention. In particular, its complex magnetic phase diagram—as a result of tuning with magnetic field or pressure—is not well-understood. From a chemical perspective, a range of lattice parameter values have been reported, suggesting a possibility of a considerable homogeneity range, i.e., UCd11–x. In this work, we perform a simultaneous study of crystallographic features coupled with measurements of physical properties. This work sheds light on the delicate relationship between the intrinsic crystal chemistry and magnetic properties of UCd11.


INTRODUCTION
The initial interest in the compounds of cadmium and uranium was motivated by the possible application of these materials in reprocessing of nuclear fuels. 1,2 Within the uranium−cadmium system, only one compound has been reported so far� denoted as UCd 11 (structure type BaCd 11 ). 1−8 Its detailed structure determination using neutron diffraction revealed strong cadmium deficiency, distributed more or less equally over all occupied Cd sites. As a result, the cadmium-deficient composition of UCd 9.5 was reported. 9 Measurements of magnetic properties of UCd 11 revealed that this compound orders antiferromagnetically below T N = 5 K. 10−12 However, what has really spiked scientific interest in this material was an enhancement of the effective electron mass, as evidenced by one of the largest electronic specific heat coefficients γ among known uranium-based materials. 9,10 From the specific heat data, γ of approximately 950 mJ mol −1 K −2 has been estimated. 10,13,14 However, de Haas−van Alphen experiments performed later 15 have suggested that such a large value of γ is likely caused by the magnetic specific heat rather than by heavy quasiparticles. Based on the de Haas−van Alphen measurements, γ in the antiferromagnetic state was estimated to be approximately 250 mJ mol −1 K −2 . 15 The uranium−uranium distance in UCd 11 is rather large (d U−U = 6.56 Å), much larger than the Hill limit (d U−U = 3.5 Å) 16 �this is consistent with the localized nature of f-orbitals in this material. 17−19 However, the magnetic phase diagram of UCd 11 appears to be rather complex: in addition to the antiferromagnetic transition, another weaker transition is observed around T = 2 K. 20,21 Moreover, upon application of modest hydrostatic pressure (p ≤ 20 kbar), two additional transitions appear below the ambient-pressure antiferromag-netic one. 22,23 Similarly, several metamagnetic transitions have also been observed. 20,21,24 The nature of all of these transitions remains unclear. Overall, while μSR spectroscopy and neutron diffraction experiments on UCd 11 confirmed bulk magnetic ordering below T N , 9,25 the properties of this material appear to be rather intricate and remain to be understood completely. 11,9,13,18,21,26 Atomic arrangement in UCd 11 , assuming complete occupancy of all Cd sites, is fairly complex, hosting uraniumcentered polyhedra coordinated by 20 cadmium atoms, see Figure 1. Four cadmium sites and one uranium site exist in UCd 11 . 9 It is likely that the origin of peculiar magnetism in UCd 11 stems from its complex crystal structure (Figures 2). A large span of lattice parameter values is reported in the literature (9.248 Å ≤ a ≤ 9.29 Å), suggesting a possible homogeneity range as a result of partial occupancy on the cadmium sites. 1,10,11,[9][10][11][12][13][14]23 Additionally, a variation of electronic specific heat coefficient γ from 803 to 950 mJ mol −1 K −2 has been observed. 10,13,14 Similar to other uraniumbased systems, a delicate interplay between intrinsic crystal chemistry and physical properties can only be revealed by a comprehensive analysis on both macro-and microscales. 27 Table S1) were prepared by direct reaction of the components. All sample preparation and handling were performed in the specialized laboratory equipped with an argon-filled glovebox system (MBraun, p(H 2 O/O 2 ) < 0.1 ppm). 36 Similar to previous studies, 8,11 single crystals of UCd 11 were obtained by melting (i) stoichiometric and (ii) slightly off-stoichiometric amounts of uranium (powder prepared from sheet, Goodfellow, 99.98%) and cadmium (pieces, Alfa Aesar, >99.9%). The tantalum tubes with the starting mixture of the elements were sealed under an argon atmosphere, heated to 420°C, and then slowly cooled back to room temperature at a rate of 2.5°C per hour. The resultant product was a gray, polycrystalline powder with some μm-sized crystals.

Materials Characterization.
Powder X-ray diffraction was performed on a Huber G670 imaging-plate Guinier camera with a Gemonochromator (CuK α1 , λ = 1.54056 Å). LaB 6 was used as a standard. Phase identification was done using WinXPow software. 37 For all samples, in addition to the main UCd 11 phase which is homogeneous (Figure 3), a small amount of either elemental Cd (samples 1−5) or elemental U (sample 6) is seen in the powder X-ray diffraction data (see Figure 4 and Table S2). While it is not possible to estimate the exact amount of Cd or U admixture, the relative amounts (compared to other samples in the study) were found from the ratio of the intensities of the strongest UCd 11 (2θ = 31.9 degrees) to the strongest Cd (2θ = 38.3 degrees) peaks. The lattice parameters were determined by a least-squares refinement using the peak positions extracted by profile fitting (WinCSD software 38 , Figure 5).
Small crystals on the order of ca. 30 μm were suitable for singlecrystal diffraction experiments. The diffraction data were collected using a Rigaku AFC7 diffractometer equipped with a Saturn 724+ CCD detector and a MoK α radiation source (λ = 0.71073 Å). The WinCSD 38 software packages were used for data analysis. The results of the crystallographic characterization of UCd 11 are provided in Tables 1−3 and S2. From the structural refinement, no variation in stoichiometry or occupancy was observed between various UCd 11 samples. Thus, all samples' stoichiometry is UCd 11 within experimental error bars.
For metallographic investigations, pieces of UCd 11 samples were embedded into a polymer matrix using a hot mounting press (ProntoPress 10). SiC paper and diamond powder with grain sizes of 3 μm or smaller were used for surface polishing. Chemical composition was studied on polished samples using energy-dispersive X-ray spectroscopy with a Jeol JSM 6610 scanning electron microscope equipped with an UltraDry EDS detector (Thermo Fisher NSS7). The semiquantitative analysis was performed with 25 keV acceleration voltage and ≈3 nA beam current. The resultant backscatter electron micrograph is shown in Figure 3. Aside from cavities (black), no inclusions of secondary phases have been detected. Elemental mapping of Cd (panel (b)) and U (panel (c)) indicates that the uranium content remains constant within the sample (8.5 at. % of U).

Physical Property
Measurements. The analysis of magnetism in UCd 11 was performed on polycrystalline samples. For  most of the samples, either elemental U or Cd was present in addition to the UCd 11 phase (see Figure 4). The magnetic properties were studied using a Quantum Design (QD) Magnetic Property Measurement System for the temperature range from T = 1.8 K to T = 300 K and for applied magnetic fields up to H = 7 T. The specific heat data were collected on a Quantum Design Physical Property Measurement System in the temperature range from T = 0.4 K to T = 10 K for magnetic fields up to H = 9 T. Due to the polycrystalline powder-like nature of the samples, it was not possible to carry out electrical resistivity measurements.

RESULTS AND DISCUSSION
The UCd 11 compound crystallizes in the cubic BaHg 11 structure type and decomposes peritectically at T = 473°C. 1 It was previously shown that the structure of UCd 11 is rather robust against application of pressure�the unit cell can be compressed by nearly 20% (for p = 20 GPa) without any discernible structural phase transitions. 26 While some structural information has been reported previously, the possibility of a homogeneity range in UCd 11 has not been investigated. 1,10,11,[9][10][11][12][13][14]23 In the current study, high-quality single-crystal data was obtained for crystals extracted from samples 4 and 5. The collection of diffraction intensities was made on an irregular single crystalline specimen with dimensions of 12 × 12 × 30 μm 3 . Crystallographic information for the single-crystal UCd 11 (sample 4), together with further details of the single-crystal Xray diffraction experiment, are presented in Tables 1 and 2. The collected diffraction data were indexed using the cubic lattice with the lattice parameter of 9.2970(3) Å, being close to the upper limit of those reported earlier (9.248 Å ≤ a ≤ 9.29 Å). 1,10,11,[9][10][11][12][13][14]23 The extinction conditions in the measured data set agreed well with the primitive lattice of the BaHg 11 structure type indicated in ref 9. Application of the chargeflipping technique allowed to establish the basic atomic arrangement formed by one uranium and four cadmium positions (Figure 1, top). It is important to note that the displacement parameter for the Cd2 position was strikingly large in comparison with three other cadmium sites.
Refinement of this structure model using anisotropic approximation of atomic displacement revealed strong anisotropy of the atomic displacement for the Cd2 site. Calculation of the residual electronic density with isotropic displacement for this position indicates nondescribed density on both sides of the position along the space diagonal of the unit cell (Figure 1, middle), making a split necessary (Figure 1, bottom). The final refinement resulted in R F of 0.033 for 579 reflections used. The attempts to resolve this split by lowering   Tables 2, 3, and S2, respectively. The crystal structures of the BaHg 11 structure type are usually described as a packing of the large cation-centered polyhedrons (UCd 20 in the case of UCd 11 ) with 20 vertices located at (0 1 / 2 1 / 2 ) and Cd-centered cuboctahedrons (CdCd 12 ) at (0 0 0)�see, for example, Figure 2   The shown error bars are the standard deviation multiplied by a factor of three. While it is not possible to determine the exact amount of elemental Cd or U within our samples, the relative amount is estimated from the powder X-ray data (see the Methods section for details).     43 and PuGa 6 . 44 The split of Cd2 position in UCd 11 can be understood as a result of the structural transformation according to the latter scenario. Similar strong displacement anisotropy was observed in the ternary derivative YbPd 3 Ga 8 45 but not in the prototype BaHg 11 . 40 The strong displacement anisotropy of the Cd2 position may have two origins: the dynamic and the static one. Independently of the origin, the Cd2 position or its split positions is 3.8 Å apart from the U one. Thus, this should not significantly influence the electronic state of U and, therefore, its magnetic moment. On the other hand, if the Cd positions located in the first coordination sphere of U are not fully occupied, as proposed by ref 9, the magnetic properties of uranium may change. The comparison of the magnetic susceptibility measurements of current and previous works reveals the same ordering temperature and effective magnetic moment (see below), which indicates that the electronic state of uranium is in fact the same across all UCd 11±x samples reported so far.
Partial occupancy on the Cd sites has been previously suggested, resulting in UCd 9.5 composition. 9 It is important to note that the analysis of the crystal structure of UCd 11 in ref 9 was carried out using neutron powder diffraction experiments. The sample investigated in ref 9 shows the lattice parameter on the lower end of the spectrum of known values (Figure 5a). It was not possible to reproduce this value of the lattice parameter in the current study�the single-crystal investigations yielded larger lattice parameter values. It is possible, however, that the defects on Cd sites reported in ref 9 may appear due to the thermal treatment during the single-crystal growth.
Magnetic properties of UCd 11 have been previously studied using a number of experimental techniques. 10−12 The entrance into antiferromagnetic state is marked by a characteristic anomaly around T N = 5 K. For all samples from the current study, a cusp-like feature has been observed in temperaturedependent magnetization data at T = 5.1 ± 0.1 K, as evidenced by the derivative dM/dT, shown in Figure 6a (see also Table  S1). Assuming that with a larger lattice parameter, the composition is the stoichiometric one and the structural deformation takes place in the cube-like arrangement in the middle of the unit cell, the low lattice parameter can produce defects in the cadmium sub-lattice. The resultant structural deformation does not influence the magnetic behavior, since the affected part of the Cd framework is located far from the uranium atoms (∼3.8 Å). Magnetism of UCd 11 is likely mediated by the RKKY interactions, which means that the magnetic susceptibility is not influenced by the crystallographic point defects. However, the cubic symmetry of the uranium coordination is locally violated, which leads to reduced peak sharpness in the dM/dT data. The inverse susceptibility data were fit to the Curie−Weiss law. In agreement with previous work, 10 an effective moment μ eff = 3.43 μ B F.U. −1 and Weiss temperature θ W = −23 K were established.
The antiferromagnetic ordering of UCd 11 is also marked by an anomaly in the specific heat data, as shown in Figure 6b. The sharpness of this feature is somewhat reduced compared to some of the previous reports, which can likely be attributed to the polycrystalline nature of the samples. The height and position of the jump are comparable to previous stud-ies. 10,13,14,21 In the normal state, the specific heat data, scaled by temperature, can be fitted with a linear relation, yielding the value of the Sommerfeld coefficient γ. For the present study, the range of γ values 860 mJ mol −1 K −2 ≤ γ ≤ 920 mJ mol −1 K −2 is consistent with previous reports.

CONCLUSIONS
In the current work, we present a detailed study of crystallographic properties of UCd 11 . We have prepared and characterized a series of UCd 11 samples grown from both uranium-rich and cadmium-rich sides of the binary phase diagram. Given that only one uranium−cadmium compound has been reported so far, all of the studied samples contain either elemental cadmium or elemental uranium in addition to the UCd 11 phase (see Figure 5b). Contrary to the literature data, we find a rather small span of the lattice parameter values. This suggests that the homogeneity range of UCd 11 is likely narrow. Additionally, the occupancy of the uranium-centered polyhedra appears to be complete, contrary to the previous report. 9 The value of the electronic specific heat coefficient γ for UCd 11 , extracted from the specific heat data above the